2.
| A | B | C | D | E | F | G | H |
| A | - | 27 | 51 | 32 | 29 | 23 | 47 | 40 |
| B | 27 | - | 24 | 35 | 20 | 42 | 33 | 28 |
| C | 51 | 24 | - | 37 | 43 | 31 | 26 | 34 |
| D | 32 | 35 | 37 | - | 39 | 45 | 44 | 30 |
| E | 29 | 20 | 43 | 39 | - | 38 | 45 | 55 |
| F | 23 | 42 | 31 | 45 | 38 | - | 53 | 45 |
| G | 47 | 33 | 26 | 44 | 45 | 53 | - | 39 |
| H | 40 | 28 | 34 | 30 | 55 | 45 | 39 | - |
The table represents a network that shows the average journey time, in minutes, between eight towns, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F } , \mathrm { G }\) and H .
- Use Prim's algorithm, starting at A , to find the minimum spanning tree for this network. You must clearly state the order in which you select the edges of your tree.
- Draw the minimum spanning tree using the vertices given in Diagram 1 in the answer book.
- State the weight of the minimum spanning tree.